The goal of most bipedal robotics research is to develop methods of achieving a dynamically balanced gait. Most current approaches focus on maintaining the balance of the system. This paper introduces a measure called the foot placement estimator (FPE) to restore balance to an unbalanced system. We begin by developing a theoretical proof to define when a biped is stable, as well as defining the region in which stability results are valid. This forms the basis for the derivation of the FPE. The results of the FPE are then extended to a complete gait cycle using the combination of a state machine and simple linear controllers. This control system is applied to a detailed and realistic simulation based on a physical robot currently under construction. Utilizing the FPE as a measure of balance allows us to create dynamically balanced gait cycles in the presence of external disturbances, including gait initiation and termination, without any precalculated trajectories.

Figures

Simulation results of the biped walking in the presence of external disturbances. The dashed portions of the feet position indicated when the foot is off the ground, and the solid portions indicated when the foot is on the ground.

A phase portrait of a simple biped using the parameters of the biped in Sec. 7 and β=60deg. The dotted line is the union of the three stable regions. The white region is the intersection of the regions of validity.

A simplified biped stepping relative to the FPE. (a) Stepping closer than the FPE results in falling forward. (b) Stepping further than the FPE causes the biped to fall back onto the swing leg. (c) Stepping precisely at the FPE will perfectly balance the COM above the standing foot.

Simulation results from gait initiation through 15 steps to gait termination. The dashed portions of the feet position indicated when the foot is off the ground, and the solid portions indicated when the foot is on the ground.

Return to: Introduction of the Foot Placement Estimator: A Dynamic Measure of Balance for Bipedal Robotics

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